You are asked to apply Hierarchical Clustering to a dataset with mixed types of data (categorical and numerical). What challenges could arise and how would you tackle them?
- All of the above
- Computationally intensive clustering
- Difficulty in defining a suitable distance metric
- Inaccurate clustering due to the scale of numerical features
The primary challenge in clustering mixed types of data is defining a suitable distance metric that can handle both categorical and numerical features. You may need to standardize numerical features and find appropriate ways to measure distances for categorical attributes (e.g., using Gower distance). This choice will significantly influence the quality and interpretability of the clustering.
How is the amount of variance explained calculated in PCA?
- By dividing each eigenvalue by the sum of all eigenvalues
- By multiplying the eigenvalues with the mean
- By summing all eigenvalues
- By taking the square root of the eigenvalues
The amount of variance explained by each principal component in PCA is calculated by dividing the corresponding eigenvalue by the sum of all eigenvalues, and often expressed as a percentage.
You're working with a dataset that has clusters of various shapes and densities. Which clustering algorithm would be best suited for this, and why?
- DBSCAN
- Hierarchical Clustering
- K-Means
- Mean Shift
DBSCAN is best suited for clusters of various shapes and densities, as it's a density-based clustering method and doesn't rely on spherical assumptions about the data.
How do hyperplanes differ in hard-margin SVM and soft-margin SVM?
- Color difference
- Difference in dimensionality
- Difference in size
- Flexibility in handling misclassifications
Hard-margin SVM does not allow any misclassifications, while soft-margin SVM provides flexibility in handling misclassifications.
How are rewards and penalties used to guide the learning process in reinforcement learning?
- To group data based on similarities
- To guide the agent's actions
- To label the data
- To reduce complexity
In reinforcement learning, rewards and penalties guide the agent's actions, encouraging beneficial behaviors and discouraging detrimental ones.
The __________ function in Logistic Regression models the log odds of the probability of the dependent event.
- Linear
- Logit
- Polynomial
- Sigmoid
The Logit function in Logistic Regression models the log odds of the probability of the dependent event occurring.
What are the potential challenges in determining the optimal values for Epsilon and MinPts in DBSCAN?
- Difficulty in selecting values that balance density and granularity of clusters
- Lack of robustness to noise
- Limited flexibility in shapes
- Risk of overfitting the data
Determining optimal values for Epsilon and MinPts in DBSCAN is challenging as it requires a careful balance between the density and granularity of clusters. Too large Epsilon can merge clusters, while too small can create many tiny clusters. Selecting MinPts affects the required density, making this tuning a complex task.
Explain how the F1-Score is computed and why it is used.
- Arithmetic mean of Precision and Recall, balances both metrics
- Geometric mean of Precision and Recall, emphasizes Recall
- Harmonic mean of Precision and Recall, balances both metrics
- nan
F1-Score is the harmonic mean of Precision and Recall. It helps balance both metrics, particularly when there's an uneven class distribution. It's often used when both false positives and false negatives are important to minimize.
Why is Bootstrapping an essential technique in statistical analysis?
- It allows training deep learning models
- It enables the estimation of the distribution of a statistic
- It provides a method for feature selection
- It speeds up computation
Bootstrapping is essential in statistical analysis because it allows estimating the distribution of a statistic, even with a small sample. By repeatedly resampling with replacement, it creates numerous "bootstrap samples," enabling the calculation of standard errors, confidence intervals, and other statistical properties.
What is the role of a decision boundary in classification problems?
- Separating classes in the feature space
- Separating data into clusters
- Separating features
- Separating training and test data
A decision boundary is a hypersurface that partitions the underlying feature space into classes. It plays a crucial role in determining the class label of a new data point based on which side of the boundary it lies.